I am a condensed matter theorist. My research
consists of using ab initio techniques,
mainly
density functional theory (DFT), to study interesting materials
systems. In principle, DFT is an exact way to rewrite the many-body Schrodinger's
equation, allowing one to solve
for the ground state energy and charge density of a given configuration of atoms;
although in practice it requires approximations. See the wikipedia entry on
DFT for more information

Here is a brief introduction to some topics I have previously studied at Rutgers and Yale. See my publication list for detailed information.

1. Chern insulators (quantum anomalous Hall insulators).

2. High-throughput searches for new functional materials.

4. Advanced Surface Chemistry.

At a
general level, the properties of most condensed matter systems are
determined by their symmetries. For instance, a material with
broken inversion symmetry can have a spontaneous polarization and a first-order response to an electric field.
Topological condensed matter systems differ in that some of their
properties are determined instead by a bulk topological invariant,
which is consists of an integral over k-space of some
function of the phase of the wavefunction. In insulators, these
topological invariants are guaranteed to be integers, which allows us
to classify insulators by their topology.

While there has been great success in finding 2D and 3D time-reversal invariant topological insulators, the first proposed topological insulators (Haldane 1988), known as Chern insulators or quantum anomalous Hall insulators, are only just now beginning to be studied experimentally. A Chern insulator, like a system which displays the integer quantum Hall effect, is a system with a non-zero Chern number. Chern insulators will display many of the interesting properties of the integer quantum Hall effect, including quantized dissipationless spin-polarized edge states, but without the strong external magnetic fields and low temperatures required by the quantum Hall effect.

In order to have a robust non-zero Chern number, a system must have broken time reversal symmetry and strong spin-orbit coupling. Previous attempts to construct such a combination have largely consisted of doping a time-reversal invariant topologically non-trivial material with magnetic atoms, to push the material into a state with non-trivial Chern number; however these attempts have proven very difficult experimentally.

We propose instead to directly combine spin-orbit with magnetism by depositing heavy atoms (e.g. Pb) onto the surface of a normal magnetic insulator (e.g. MnTe). The advantages of this approach are that it does not require doping, it guarantees that the spins are aligned, and it features atoms with the strongest possible spin-orbit coupling. We have verified this approach using first principles calculations, finding many Chern insulators including some with large band gaps, and we suggest a combined first principles / experimental search to find an experimentally realizable Chern insulator. See our paper for details.

Figure: Geometry of a proposed Chern insulator. 2/3 ML Pb on A-type antiferromagnetic MnTe.

Many of the technological challenges facing the world today are in fact materials challenges. In the energy sector, photovoltaics, batteries, hydrogen strorage, etc., all require better, faster, lighter, and cheaper materials. Furthermore, pushing beyond the limits of traditional silicon-based field effect transistors and magnetic storage requires new materials which can be used as high-k dielectrics, high-mobility semiconductors, ferroelectrics, piezoelectrics, multiferroics, etc.

First principles theoretical techniques have advanced to the point that the properties of many materials can be calculated accurately and efficiently, without input from experiment, making these techniques ideal for scanning large numbers of both previously synthesized and novel materials for interesting and useful properties. In a high-throughput search, the properties of an entire classes of materials can be analyzed in order to find examples which have ideal properties for any given application. These candidate materials can then be synthesized, characterized, and hopefully applied.

One
particularly useful property a material can have is a strong response
to an electric field. A ferroelectric is a material which has a
polar ground state, the direction of which can be switched with in an
electric field. Closely related to ferroelectrics are
antiferroelectrics, which are materials with an anti-polar ground state;
however, they also have a low energy polar state which can be switched
to in an electric field.

Figure: Schematic of antiferroelectrics

Perovskite
oxide ferroelectrics and to a lesser extent antiferroelectrics have
been studied extensively; however, in many cases their properties are
not ideal for applications. We have used high-throughput
techniques to discover
and study new classes of ABC semiconducting hexagonal ferroelectrics
and antiferroelectrics. These materials have a variety of
advantages over traditional ferroelectrics and antiferroelectrics,
including uniaxial polarization, large band gap ranges (including
semiconductors), and different shapes and chemistries which should
allow them to interface with more materials. See here and here for more details.

Figure: ABC ferroelectrics and antiferroelectrics

I am also involved in techniques for doing high-throughput calculations, see the section on pseudopotentials.

Oxides,
and in particular perovskite oxides, provide the opportunity for a wide
range of functionality, including ferroelectrics, antiferroelectrics,
ferromagnets, multiferroics,
high-k materials, superconductivity, etc. However, by combining
different perovskite oxides, it is possible to achieve even greater
functionality, examples of which include 2D electron gases at
polar/non-polar interfaces (SrTiO_{3}/LaAlO_{3}) and improper ferroelectricity (see here or here).

I have studied theoretically the coupling of phonons from a SrTiO_{3} (STO) substrate into a La_{0.5}Sr_{0.5}MnO_{3} (LSMO) thin film, which was previously grown by the Ahn group
at Yale. When STO goes through its phonon-softening phase
transition, its phonons couple strongly to the LSMO, affecting the LSMO's
magnetism and conductivity. Based on first principles calculations, I created a classical model of the
force-constants in these materials and used finite-temperature Monte
Carlo to analyze this effect as a function of temperature. This
type of strong interfacial phonon coupling provides an interesting new
probe to study oxide systems. See here for more details.

Figure: Top- geometry of LSMO/STO interface. Bottom- low freqency phonon eigenvector extends into LSMO.

Ferroelectric
materials have a strong, persistent response to an electric field,
and their surfaces provide an opportunity to use this response to do
advanced chemistry. For instance, one could bind molecules to the
positively-poled surface, encouraging a chemical reaction, and then
switch the polarization to release the products. Studying these
complicated reactions requires careful analysis of surface
thermodynamics and kinetics. As a proof of principle, I have studied
the binding of H_{2}O and CO_{2} to the PbTiO_{3} surface under positive and negative polarization, finding a variety of changes upon polarization reversal. See here or our review for more details.

Figure: Bonding of CO_{2} to TiO_{2}-terminated PbTiO_{3} surface. Electrons move to blue regions due to bonding.

My
earliest work consisted of studying the deposition of submonolayer
coverages of Sr and La onto Si (001) and Ge (001). These
technologically relevant surfaces are the first step in growing complex
oxides on Si. In collaboration with the Ahn group and Altman group
at Yale, I determined the structure of the 1/6 ML Sr on Si and Sr on Ge
structures. These structures have been been studied/confirmed
experimentally by STM, and understanding these complex surface
reconstructions has helped improve oxide growth on
semiconductors. See our review here.

Figure: Structures of submonolayer Sr on semiconducting surfaces.